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A047079 a(n) = Sum_{i=0..floor(n/2)} A047072(i, n-2*i). 3
1, 1, 2, 3, 3, 4, 7, 9, 14, 23, 33, 52, 85, 127, 202, 329, 503, 804, 1307, 2027, 3250, 5277, 8263, 13276, 21539, 33957, 54638, 88595, 140373, 226108, 366481, 582865, 939622, 1522487, 2428517, 3917412, 6345929, 10145769, 16374126 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==n, 2*CatalanNumber[n-1] +2*Boole[n==0], If[k>n, Binomial[n+k-1, n] -Binomial[n+k-1, n-1], Binomial[n+k-1, k] -Binomial[n+k-1, k- 1]]];
A047079[n_]:= Sum[T[j, n-2*j], {j, 0, Floor[n/2]}] +Boole[n==0];
Table[A047079[n], {n, 0, 50}] (* G. C. Greubel, Oct 29 2022 *)
PROG
(Magma)
b:= func< n | n eq 0 select 1 else 2*Catalan(n-1) >;
function A(n, k)
if k eq n then return b(n);
elif k gt n then return Binomial(n+k-1, n) - Binomial(n+k-1, n-1);
else return Binomial(n+k-1, k) - Binomial(n+k-1, k-1);
end if; return A;
end function;
[(&+[A(j, n-2*j): j in [0..Floor(n/2)]]): n in [0..50]]; // G. C. Greubel, Oct 29 2022
(SageMath)
def A047072(n, k): # array
if (k==n): return 2*catalan_number(n-1) + 2*int(n==0)
elif (k>n): return binomial(n+k-1, n) - binomial(n+k-1, n-1)
else: return binomial(n+k-1, k) - binomial(n+k-1, k-1)
def A047079(n): return sum( A047072(j, n-2*j) for j in range(((n+1)//2)+1) )
[A047079(n) for n in range(51)] # G. C. Greubel, Oct 29 2022
CROSSREFS
Sequence in context: A327134 A140514 A240209 * A207624 A203990 A238812
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name improved by Sean A. Irvine, May 11 2021
STATUS
approved

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Last modified April 18 22:18 EDT 2024. Contains 371782 sequences. (Running on oeis4.)